Linear valuation without OLS: the Theil-Sen estimation approach

Abstract

OLS-based archival accounting research encounters two well-known problems. First, outliers tend to influence results excessively. Second, heteroscedastic error terms raise the specter of inefficient estimation and the need to scale variables. This paper applies a robust estimation approach due to Theil (Nederlandse Akademie Wetenchappen Ser A 53:386–392, 1950) and Sen (J Am Stat Assoc 63(324):1379–1389, 1968) (TS henceforth). The TS method is easily understood, and it circumvents the two problems in an elegant, direct way. Because TS and OLS are roughly equally efficient under OLS-ideal conditions (Wilcox, Fundamentals of modern statistical methods: substantially improving power and accuracy, 2nd edn. Springer, New York 2010), one naturally hypothesizes that TS should be more efficient than OLS under non-ideal conditions. This research compares the relative efficiency of OLS versus TS in cross-sectional valuation settings. There are two dependent variables, market value and subsequent year earnings; basic accounting variables appear on the equations’ right-hand side. Two criteria are used to compare the estimation methods’ performance: (i) the inter-temporal stability of estimated coefficients and (ii) the goodness-of-fit as measured by the fitted values’ ability to explain actual values. TS dominates OLS on both criteria, and often materially so. Differences in inter-temporal stability of estimated coefficients are particularly apparent, partially due to OLS estimates occasionally resulting in “incorrect” signs. Conclusions remain even if winsorization and the scaling of variables modify OLS.